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A NOTE ON RELATIVE PSEUDOCOMPACTNESS IN THE CATEGORY OF FRAMES

Part of: Boolean algebras (Boolean rings) Distributive lattices Maps and general types of spaces defined by maps

Published online by Cambridge University Press:  22 May 2012

THEMBA DUBE
THEMBA DUBE*
Affiliation:
Department of Mathematical Sciences, University of South Africa, PO Box 392, 0003 Pretoria, South Africa (email: dubeta@unisa.ac.za)
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Abstract

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A subspace S of Tychonoff space X is relatively pseudocompact in X if every f∈C(X) is bounded on S. As is well known, this property is characterisable in terms of the functor υ which reflects Tychonoff spaces onto the realcompact ones. A device which exists in the category CRegFrm of completely regular frames which has no counterpart in Tych is the functor which coreflects completely regular frames onto the Lindelöf ones. In this paper we use this functor to characterise relative pseudocompactness.

Keywords

frameframe homomorphismreal-valued continuous functions on a frameLindelöf coreflectionrelative pseudocompactness

MSC classification

Secondary: 06D22: Frames, locales 54C40: Algebraic properties of function spaces

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 87 , Issue 1 , February 2013 , pp. 120 - 130
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

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